I've had someone claim personal injury against my insurance company before (my fault, me being a tosser), but that in itself doesn't raise my insurance premium (I don't think).
What did raise my premium was the fact that I claimed, and I'll be paying that back for a few years to come.
I hardly knew about the fact the person I crashed into claimed, and IMO they were perfectly entitled to it. Thats the reason I pay insurance, and its the risk that the insurance companies take. All in all, they make money and probably lots of it.
EDIT: I think the difference is that these people are claiming against an insurance company, its their business to insure people. Part and parcel of that is that occasionally people will put in claims and they'll take that into consideration when working out premiums. If it were a person claiming against an individual or a business (like you see on telly) then I'd agree with Tomm.